Deep within the Facebook campus, 30 miles south of San Francisco, Sheryl Sandberg is posing for photos. It is not her favourite activity. "You can just fix everything, right?" she says to Patrick, the photographer. "I don't want to look super-uncomfortable, like I usually do in pictures. I'm not a model type, I'm a suburban mom, so nothing too fashiony." As Patrick talks, Sandberg murmurs "hmm-hmm-hmm", as if to hurry him along. "Fast is good," she says before breaking suddenly into laughter.

It is a different version of Sandberg I meet today from the one I met here a year ago, when Lean In, her polemic about female leadership, had just been released. Then, the 44-year-old seemed rattled, both by the scale and tenor of the book's reception. She gave interviews with the rictus of the corporate achiever, bound to the script and on-message.

Since then, a huge amount has been written about her, some of it fair, much of it unfair, all of it focused on whether someone in her position of extraordinary privilege – earlier this year, according to Forbes magazine, Sandberg became one of only 172 female billionaires in the world – can reasonably offer advice to the rest of us. The book, which gives practical tips to women on how to overcome structural biases in the workplace, has been both lauded and slated, but either way jammed on the bestseller lists for a solid 12 months.

Sandberg, meanwhile, has been on what she would almost certainly call a steep learning curve, encountering hostility from a quarter she clearly didn't anticipate before the book came out – not conservative men in the business world, but other feminists, many of whom have resented her ahistorical and largely apolitical approach to the subject and Lean In's occasionally infuriating guilelessness; its general air of having hit upon this travesty called inequality in the work place.

In response, Sandberg has learned to talk fluently about race and class – "women of colour" is now part of her lexicon – and, in the new graduate edition of the book, to address some of Lean In's perceived shortfalls. It is an irony that, while describing how women tend to internalise criticism, Sandberg has herself come in for harsh review and her manner today would suggest she has taken at least some of it to heart. "Do I look friendly?" she says to Patrick at the end of the shoot. He assures her that the photos look great. "Make sure it's friendly not scary," Sandberg says and keeps up a giggly, slightly manic cheerfulness throughout the interview, which is, I think, an over-correction to charges of coldness. The woman can't win. Whether or not Sandberg is "friendly" should, of course, be neither here nor there; Mark Zuckerberg, her boss at Facebook, is not judged on the strength of his chummy interpersonal skills. Neither does his wealth offend in quite the way hers does. The money makes Sandberg unpalatable to lots of people at an almost conceptual level, disqualifying her from the realm of regular womankind, and as a result she dodges questions about her fortune with the skill of a politician.

She would rather talk about initiatives such as the Lean In circles, which she has been travelling the world promoting for the last year. She would even rather talk about her divorce, at the age of 24. She is now married to David Goldberg, the CEO of another billion-dollar company, SurveyMonkey, and they have two children. Part of the book hinged on how Sandberg plucked up the courage to leave the office at 5.30pm so she could see them for a few hours before they went to bed, getting back on her BlackBerry later in the evening.

She also wrote about how, precisely, she negotiated the stock options package when she signed on at Facebook, which has made her so wealthy. As Sandberg points out, women are bad at negotiating on their own behalf, particularly when it comes to pay. All of which strikes me as useful, the more so for coming from someone within the corporate world, who is preaching mostly to the unconverted.

If there is a scepticism about Sandberg, it is tied up with a more general cynicism about Facebook and its mission. Posters in the reception area encourage the kind of self-regard you find only in Californian tech companies and corners of Westminster: a photo of Nelson Mandela with the slogan Open The Doors; the legend What Would You Do If You Weren't Afraid?; and a collection of bumper sticker-type sentiments such as Meetings Were Made For Laughter. If you worked here, the pressure to be inspired all the time might turn you mad.

It's the tone, unsurprisingly, that also motors Lean In, which is full of chipper exhortations to roll up your sleeves and get on with it. Sandberg does not come from inherited wealth, which makes her unusual in the Forbes billionaire list. She is from a middle-class home in Florida, her mother a teacher, her father an ophthalmologist, a socially concerned and vaguely lefty-sounding family. "I came from parents who spent their lives speaking out, for political prisoners in the Soviet Union and victims of religious persecution." They also encouraged her to marry early, on the basis that, as she writes in the new introduction to Lean In, all the "good ones" get snatched up in college. Sandberg believed them, and it resulted in her marrying too early, to a businessman called Brian Kraff, and a year later getting a divorce.

This runs somewhat counter to the Facebook self-image. From the board down, staff are encouraged to think of themselves as outliers and visionaries, something built into the very fabric of the company, and at odds with the very conventional roots of much of the top brass. (Andrea Saul, who runs the Lean In communications team for Sandberg, was hired after managing publicity for Mitt Romney during his 2012 presidential campaign.) If anything, this makes Lean In more not less impressive. In the context of the deeply conservative business world, its message constitutes a radical departure.

Which has not, historically, been Sandberg's MO. From adolescence onwards, she has hit every establishment mark: a degree in economics followed by an MBA at Harvard; a prestigious internship as research assistant to Larry Summers, her former thesis adviser and then chief economist of the World Bank; a stint at McKinsey, the management consulting firm. And ultimately, five years as Summers' chief of staff after he became secretary to the treasury under Bill Clinton in 1995.

On paper at least, except for a brief, jaunty stint as an aerobics instructor while at college, Sandberg's conscientiousness is overwhelming. Has she ever, in her life, got drunk and thrown up in a cab? Or called in sick from a hangover?

"Yes and yes," she says, laughing wildly.

When?

"Look, I was a high-school kid, a college kid like others. There was a part of me that's glad fewer people had cell phones when I was that age. I haven't had all these successes – the hardest thing for me to write in the book was about my divorce. I married a wonderful man and I was just too young. But at the time, you know, no one in our family had ever got divorced. It was shameful. It felt like a failure. You go on a date when you're 25 and you've been divorced? It's a big thing. How do you bring that up? Do you bring that up? Is it too weird? I lived with that for a long time."

She also lacked confidence during the early stages of her career, something Sandberg attributes partly to gender. At college, she was slow to put up her hand during discussions. At the World Bank, she dithered around, as everyone who has done work experience has, in a state of dire under-employment and agonising shyness.

"I was embarrassed," she says. "I thought, well, it must be my fault. Obviously if anyone thought I was good at anything, they'd give me something to do. I remember there was a library that I could sneak off to and pretend to be busy. And finally I thought, wait a second. I could ask for things to do, but that felt weird. But then I just started doing stuff and that worked. If I'd been a man, would I have walked in thinking 'I'm awesome'? Maybe." The new graduate edition of Lean In is designed to call a generation to awareness. In the spirit of forewarned is forearmed, Sandberg writes about women being less willing to take risks than men, and of the way in which their failures are held more seriously against them.

Has Sandberg ever thrown up in a cab or called in sick with a hangover? ‘Yes and yes,’ she says, laughing wildly. Photograph: Patrick Fraser for the Guardian Patrick Fraser/Guardian

Her own risks, it turned out, paid off. After Clinton left office, Summers and Sandberg were out of work, and she made what, at the time, was a bold decision: to go west, to California, and take a job with Google, as VP of global online sales.

"It wasn't obvious. Look, I had great opportunities, and against my own advice in the book, I've been really lucky and got help from others. I'm lucky that I was born to parents who emphasised education and could afford to send me to college – all things I think everyone should have. When I moved to Silicon Valley, it was after the crash. It was not obvious this would be a good thing. And when I went to Facebook, most people thought it was a crazy move."

The move to Facebook came eight years later, when it was still a relatively small company and nothing like the rocket ship it became. What was she acting on? "Two things: belief in what Facebook was doing; and getting to know Mark. I just believed. I believed that the technology would change people's lives. I believed putting real identity online – putting technology behind real identity – was the missing link. I'd worked on leprosy and malaria in India [at the World Bank] and asked myself the question: why do we let 2 million children die every year around the world for not having clean water? Because they're faceless and nameless. So, for me, Facebook looked like it was going to solve the problem of the invisible victim."

Not long after Sandberg joined Facebook, the company threw one of its themed lunch events to which all staff were invited. It was taco day, and Sandberg, approaching the line for food, stood for a moment to take in the scene. "There was the taco stuff, and then there was this bar for the fixings," she says. The staff members, observed Sandberg, were taking too long with the fixings [toppings] and creating a bottleneck. "And I watched this and thought, this is ridiculous. I said, 'Excuse me, everyone!' And I made the fixings bar into a double line. And the line started moving and everyone was like, yeah!" She laughs. "It was one of those moments when I think people were a little shocked, but I gained a lot of credibility in the company."

Last year, at the Facebook summer party, there was a ride for kids. "You walked up these steps and would ride a thing down. And they wouldn't let the next kid go up until the first kid was all the way down. And there was this huge line. So I said, 'You know, if you would let the next kid go up the steps and wait up there, things would go faster.'"

It's like she has efficiency OCD, I say.

"A little bit. I may have that."

One can imagine this behaviour being described as bossy, and Sandberg has certainly been called that, from childhood onwards. Her recent campaign to "ban" the word provoked a lot of discussion and a fair amount of ridicule; the campaign itself, it was pointed out, sounded kind of bossy. What it was, in fact, was a clever piece of marketing to frame a central issue of Lean In: the stigmatisation and trivialisation of female leadership. At her live events, Sandberg likes to ask the audience to raise their hands if they have ever been called too aggressive at work. "I've never seen more than 5% of men raise their hands. Every woman I know, particularly the senior ones, has been called too aggressive at work. We know in gender blind studies that men are more aggressive in their offices than women. We know that. Yet we're busy telling all the women that they're too aggressive. That's the issue."

Data is Sandberg's oxygen. If she'd had her way, the entire book would have been full of studies of this kind and, in fact, the first draft was. ("Pages on matrilineal Maasai tribes. I had stuff in that first chapter that didn't make it into the footnotes.") It's good, solid stuff that it is gratifying to hear someone in her position articulate so strongly, when half the women you meet in public life are afraid even to identify as feminists.

And so, Sandberg says, here it is; the data on bossy, or rather what bossy signifies. "Look at a country like Norway," she says. "It has the best public policy in the world – phenomenal maternity leave, great paternity leave, quotas for women on boards and in parliament. Do you know how many women run their big companies? 3.4%. So that stereotype is alive and well everywhere in the world."

What about male-specific terms of insult such as "jerk"?

"We did some research on this; I think it's less male than bossy is female. And it doesn't correlate with leadership. Jerk is being a jerk, and women can be jerks, too. But this is about leadership. A woman who works at Facebook sent me her daughter's report card this week, which said, 'X has a tendency to be bossy.'"

Right, but when used correctly, the word bossy has a legitimate meaning, which is interfering where you're not needed or wanted. "But it's used only for girls. You do a search on 'bossy' and 'boy' through all of Google's digitised books? You get zero results, which means there are fewer than 40 mentions."

Data, as we know, explains only so much, and Sandberg has in the last year had to catch up on nuances not covered by the studies. She has tried to expand her book to include chapters from women of colour, and "women who don't want children, and different family structures and stuff", and refers critics to the Lean In website, where women across a much broader spectrum – female soldiers in Afghanistan, those on low and middle incomes – are posting accounts of their own experiences.

But class continues to be problematic and Sandberg is acutely sensitive to the charge that she's writing only for other rich women. Much of the criticism on this score strikes me as redundant; getting more women into the boardroom is a legitimate exercise, besides which, many of the lessons from Lean In are translatable, particularly those on negotiating. As Sandberg says, "We continue to expect women to be communal. So when we tell them to negotiate for themselves, they need to tie in why it's good for other people, in ways that men don't have to."

She is also smart about women and guilt. "Guilt," Sandberg says, "is fundamentally about not doing enough for other people, I think. So of course women feel more guilty, because we don't expect men to do stuff for other people. We expect men to do stuff for themselves."

It's a point of curiosity as to whether Sandberg's life outside the office bears even a passing resemblance to everyone else's. I ask whether writing the book changed the dynamic in her own home. "I think I'm more aware; of the times my daughter gets called bossy, for example. Gender kicks in early. I have to stop myself from saying to my daughter, 'You look pretty.' I would never say that to my son. I try not to, and probably do it more than I want, but I'm much more aware of it than I would have been."

The thing most couples I know argue about, once they have children, is this: who does more? Does she have that fight?

"That's right."

It's pertinent?

"Sure. With all my friends. The issue of who does more, men or women, is pertinent for everyone."

Even if you have infinite resources? She winces slightly at this, as if I have said something ungracious.

"Yeah because someone is still in charge and someone is still making decisions. You want to be there for your children, so you are doing a bunch. In the US, 4% of stay-at-home parents are men. The very concept of leisure is something that has been male-dominated for centuries. You go to a village – I've done a lot of work in villages, and women have no leisure. The women fetch the water, and men… at every income level, in every country in the world, we have managed to organise society so that men always have more leisure. I think the other thing that has been true of Lean In is that it has been much more broadly applicable than people give it credit for."

Noted. I'm not done with the personal details of her life, however, which she is firmly committed to not talking about. Does she, for example, still fly commercial?

"I don't love talking about it and here's why: it goes to the question of, how do you do it all? Which is a question we only ever ask women. This assumption that women can't. So I have resources that other people don't have and there's no question about that but…"

But it's also just a question of voyeurism into the lives of a very small number of people. I would still ask a guy who was worth…

"No one does," she interrupts. "Men aren't asked, how do you do that, how do you do this? Do you have nannies? Do you have a cook? My husband has never been asked. I am asked that all the time. And I can't find a man who's been asked. Jeff Weiner [CEO of LinkedIn] has never been asked. Here's what I would say: I have resources that other people don't have, and I know that and appreciate it. The problems are that we assume women should do more at every level. In every environment. Tina Fey wrote about it in her book. She and Steve Carell did a movie tour together. They both are actors, both have families, both have full-time TV shows. She was asked how she managed, he never was."

Of course. But when you get to a level of wealth so far above the average, it is assumed something existential happens and…

"Ask male CEOs if they've been asked this." She is wrong – you would (and many have) asked Bill Gates about his mind-boggling wealth and how he spends it. But she is also completely right; the next question would not be how many nannies does he have. Why would it? Apart from anything else, he has a wife.

One of the most impressive factors about the book and the campaign around it is that she has put her money where her mouth is. The Lean In campaign, although using Facebook infrastructure, is funded entirely by Sandberg. And, amid all the publicity, she follows her own advice on the quiet. It's a small example, this, but a female friend who was made CEO of a relatively obscure tech company in San Francisco last year, and who once met Sandberg at a party, received an email congratulating and encouraging her when the appointment was announced.

There is still the sanctimony of tone to overcome. "Thank you for caring," Sandberg says with a soppy look when we part, giving me a Clintonian squeeze at the elbow and a look of maddening condescension. But she seems also, over the last year, to have become notably and gratifyingly more strident. Sandberg is occasionally asked to talk at private members' clubs where women are not allowed to join. "I don't accept those invitations," she says.

And, although she denies having ambitions in this area, her interests have started to range beyond business to politics. "In the last senatorial election in the US, women got 20% of the seats," she says. "And all the headlines were Women Take Over the Senate. And I felt like saying, 'Dudes, hello?! Fifty percent of the population having 20% of the seats is not a takeover. It's a gap. It's a problem.'"

• Lean In: The Graduate Edition is published by WH Allen at £16.99. To order a copy for £13.59, including UK mainland p&p, go to theguardian.com/bookshop.

• This article was amended on 5 April 2014 because it originally described Sandberg as Facebook's CEO. This has been corrected.

Sheryl Sandberg may be one of the most influential executives in the world now, but there was a time when social media's bigwig was just starting out. Her first boss recalls when she was fresh out of college